Mean response estimation with missing response in the presence of high-dimensional covariates |
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Authors: | Yongjin Li Qihua Wang Liping Zhu |
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Institution: | 1. Academy of Mathematics and Systems Sciences, Chinese Academy of Sciences, Beijing, China;2. Institute of Statistical Science, Shenzhen University, Shenzhen, Guangdong, China;3. Institute of Statistics and Big Data, Renmin University of China, Beijing, China |
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Abstract: | This paper studies the problem of mean response estimation where missingness occurs to the response but multiple-dimensional covariates are observable. Two main challenges occur in this situation: curse of dimensionality and model specification. The non parametric imputation method relieves model specification but suffers curse of dimensionality, while some model-based methods such as inverse probability weighting (IPW) and augmented inverse probability weighting (AIPW) methods are the opposite. We propose a unified non parametric method to overcome the two challenges with the aiding of sufficient dimension reduction. It imposes no parametric structure on propensity score or conditional mean response, and thus retains the non parametric flavor. Moreover, the estimator achieves the optimal efficiency that a double robust estimator can attain. Simulations were conducted and it demonstrates the excellent performances of our method in various situations. |
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Keywords: | Central mean subspace Imputation Kernel regression Missing response Weighted-bandwidth |
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